NSWC/WOL TR 76-155 



as it responds to this applied pressure. Below the pressure traces are 

 corresponding sizes calculated for the spherical air bubble used to 

 represent the fish's swim bladder. 



This fluid motion can be likened to a mass attached between 

 two springs, the end of one being fixed, the end of the other movable. 



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The first spring is analogous to the internal gas pressure; the 

 second to the changing external water pressure. Let us imagine the 

 mass resting on a frictionless block of ice. It is at rest in a 

 position of equilibrium. If at t=0 we quickly displace the movable 

 spring to a new position, the mass will oscillate about a new position 

 of equilibrium determined by the displacement of the end of the spring, 

 The mass will oscillate about this new equilibrium position with an 

 amplitude equal to the displacement of this equilibrium position from 

 the initial at-rest position of the mass. 



This initial at-rest position now becomes an extremum of the 

 oscillatory motion. Since, at each extremum of the motion the mass 

 is instantaneously at rest, a subsequent jump displacement of the end 

 of the spring occurring at an extremum simply shifts the motion to an 

 oscillation about a new equilibrium position - and the new amplitude 

 is just the distance of the mass at the time of the jump from this 

 new equilibrium position. 



Likewise, for the bubble, step changes in the outside water 

 pressure occurring at half-period intervals simply change the equili- 

 brium pressure (equal to the outside pressure) of the oscillating 



19 



